Robinson's preferences between apples (a) and bananas (b) are expressed by the following:
U = (a+2)0.5(b+1)0.5
(a) Show that Robinson's indifference curves are negatively sloped.
(b) Are they convex to the origin? Explain.
a)U = (a+2)0.5(b+1)0.5
Let (a+2) be x and (b+1) be y.
U becomes;
U="x^{0.5}y^{0.5}"
"MU_{x}=0.5x^{-0.5}y^{0.5}"
"MU_{y}=0.5x^{0.5}y^{-0.5}"
"MRS=\\frac{MU_{x}}{MU_{y}}"
MRS is the slope of the indifference curve at any single point along the curve.
"=" "\\frac{0.5x^{-0.5}y^{0.5}}{0.5x^{-0.5}y^{0.5}}=\\frac{y}{x}"
b)The indifference curves will be convex to the origin because, as one consumes more of good y, they will consume less of good x.
Comments
Leave a comment